Hippopotamus optimization–tuned sigmoid PID controller for load frequency control of a two-area thermal power system with renewable energy sources
Scientific Reports, cilt.16, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1038/s41598-026-41620-1
- Dergi Adı: Scientific Reports
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, Chemical Abstracts Core, MEDLINE, Directory of Open Access Journals
- Anahtar Kelimeler: Governor dead-band, Hippopotamus optimization, Load frequency control, Renewable energy sources, Sigmoid proportional-integral-derivative controller, Two-area thermal power system
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
The increasing penetration of renewable energy sources (RES) in modern interconnected power systems introduces significant challenges for load frequency control (LFC) due to increased nonlinearities, the governor dead-band (GDB) effect, parameter uncertainties, and continuous power fluctuations. These factors reduce the effectiveness of conventional fixed-gain controllers and make it difficult to maintain frequency and tie-line power deviations within acceptable limits under varying operating conditions. To address these limitations, this study proposes a sigmoid proportional-integral-derivative (SPID) controller for LFC in a two-area thermal power system integrated with RES. In the proposed approach, the controller gains are adaptively adjusted through a sigmoid-based nonlinear mapping, and the corresponding parameters are optimally tuned using the Hippopotamus Optimization (HO) algorithm by minimizing the Integral of Time-weighted Absolute Error (ITAE) performance index. The performance of the proposed HO-SPID controller is evaluated under four time-domain scenarios: a baseline case without GDB and RES, a GDB-inclusive case without RES, a case with variable RES effects, and a robustness analysis of the baseline system under simultaneous ± 25% and ± 50% variations in all system parameters. Additionally, to demonstrate the stability of the proposed controller, frequency-domain stability is examined using Bode analysis. Simulation results demonstrate that the proposed HO-SPID controller significantly outperforms state-of-the-art PID-based metaheuristic controllers in terms of ITAE minimization, settling time, and undershoot, while the robustness analysis under parameter uncertainties and the Bode-based frequency-domain assessment jointly confirm its stable operation.